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Development (topology) — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Development_(topology)
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T18:59:18.531Z
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Development (topology) — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Development_(topology) (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_72b136dc240b (Metraipolis archive dc_72b136dc240b, sha256 8ec171664c63656100b28873b7ad8f582b569056afd56763c07aa7006f701d93)

BibTeX

@misc{dc72b136dc240b,
  title = {Development (topology) — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Development_(topology)},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_72b136dc240b; sha256 8ec171664c63656100b28873b7ad8f582b569056afd56763c07aa7006f701d93},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Development_(topology). Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In the mathematical field of topology, a development is a countable collection of open covers of a topological space that satisfies certain separation axioms. Let X {\displaystyle X} be a topological space. A development for X {\displaystyle X} is a countable collection F 1 , F 2 , … {\displaystyle F_{1},F_{2},\ldots } of open coverings of X {\displaystyle X} , such that for any closed subset C ⊂ X {\displaystyle C\subset X} and any point p {\displaystyle p} in the complement of C {\displaystyle C} , there exists a cover F j {\displaystyle F_{j}} such that no element of F j {\displaystyle F_{j}} which contains p {\displaystyle p} intersects C {\displaystyle C} . A space with a development is called developable. A development F 1 , F 2 , … {\displaystyle F_{1},F_{2},\ldots } such that F i + 1 ⊂ F i {\displaystyle F_{i+1}\subset F_{i}} for all i {\displaystyle i} is called a nested development. A theorem from Vickery states that every developable space in fact has a nested development. If F i + 1 {\displaystyle F_{i+1}} is a refinement of F i {\displaystyle F_{i}} , for all i {\displaystyle i} , then the development is called a refined development. Vickery's theorem implies that a topological space is a Moore space if and only if it is regular and developable.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «topology»).
Fonte: Wikipedia in inglese, voce «Development (topology)» — https://en.wikipedia.org/wiki/Development_(topology)
Wikidata Q5266672 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q5266672
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Development_(topology)?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1043957538, consultata il 2026-10-15T18:21:59.020Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: e92710988879fcdf2c8a3c98bbb2cec908ec294367049b65f8f8ae5e00bd84dd